This is an important and exam oriented question from Chapter name- circles
Topic – Angle properties of circles
Chapter number- 15
In first qies AB is a diameter of the circle. If ∠ADC = 120°, we have to find ∠CAB.
In the figure (ii) , sides AB and DC of a cyclic quadrilateral ABCD are produced to meet at E, the sides AD and BC are produced to meet at F. x : y : z = 3 : 4 : 5, now we have to find the values of x, y and z.
ICSE Avichal publication
Understanding ICSE Mathematics
Question 8
Solution:
(a) Construction: Join BC, and AC then
ABCD is a cyclic quadrilateral.
Now in ∆DCF
Ext. ∠2 = x + z
and in ∆CBE
Ext. ∠1 = x + y
Adding (i) and (ii)
x + y + x + z = ∠1 + ∠2
2 x + y + z = 180o
(ABCD is a cyclic quadrilateral)
But x : y : z = 3 : 4 : 5
x/y = ¾ (y = 4/3 x)
x/z = 3/5 (z = 5/3 x.